X-bar and R control chart calculator
Your data
Paste straight from a spreadsheet if you like. Every line has to carry the same number of measurements, because the constants that build the limits depend on that size.
Subgroups are meant to be taken close together in time, so that whatever varies inside one of them is the ordinary noise of the process, and whatever varies between them is the part worth investigating. Sampling five pieces made in the same minute tells you more than five taken across the week.
Results
| Measurements per subgroup | — |
| Subgroups used | — |
| Average of the subgroup means | — |
| Average range | — |
| Upper and lower limit on the chart of means | — / — |
| Upper and lower limit on the chart of ranges | — / — |
| Short-term standard deviation the ranges imply | — |
| How much wider the spread of single measurements is than the chart of means | — |
The limits on these charts have nothing to do with what the customer asked for. They are worked out from what the process actually does, which is why a point inside them can still be a bad part, and a point outside them can still be within tolerance. Drawing the tolerance on the chart is the most expensive mistake in the subject: it makes people adjust a machine that was fine, and leave alone one that has moved.
The chart of means is narrower than your data on purpose. Its limits apply to an average of several pieces, and averages vary less than pieces do, by the square root of how many went into them. Comparing a single measurement against those limits will show alarms that are not there, which is what the last row of the table is warning about.
Read the chart of ranges before the chart of means. If the spread itself is unstable, the limits on the other chart were built on a moving foundation and there is nothing to interpret yet.
Are control limits the same as specification limits?
No, and treating them as the same is the most expensive mistake in the subject. Control limits come from what the process actually does; specification limits come from what the customer asked for. They are two different things measured on the same axis.
The consequence is concrete: a point inside the control limits can still be a bad part, and a point outside them can still be within tolerance. Drawing the tolerance on the chart makes people adjust a machine that was fine and leave alone one that has moved.
Why is the chart of means narrower than my measurements?
Because its limits apply to an average, not to a single piece. An average of n pieces varies less than a single piece by a factor of the square root of n, so with subgroups of five the spread of single measurements is 2.24 times wider than the chart.
This is why comparing an individual reading against the limits of the means chart produces alarms that are not there. The page prints that factor so the difference is in front of you.
| Measurements per subgroup | Single measurements are this much wider |
|---|---|
| 2 | 1.41 |
| 4 | 2.00 |
| 5 | 2.24 |
| 9 | 3.00 |
| 10 | 3.16 |
Should I read the chart of means or the chart of ranges first?
The ranges, always. The limits on the means chart are built from the average range, so if the spread itself is unstable those limits rest on a moving foundation and there is nothing yet to interpret.
Put the other way round: an unstable range chart tells you the process is not repeating itself at all, and that has to be settled before asking whether it is centred.
Can I calculate capability from an unstable process?
You can compute the number, and it will not mean anything. Capability indices describe how a process fits a tolerance, and that description is only useful if the process will behave tomorrow the way it behaved today. An unstable process has no single spread to describe.
So the order is stability first, capability second. The standard deviation this page reports, taken from the average range, is the short-term one those indices expect, which is why it is worked out from within subgroups rather than from all the data pooled together.
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